NAG Library Function Document

nag_imldwt (c09cdc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     nwlinv – IntegerInput

On entry: the number of levels to be used in the inverse multi-level transform. The number of levels must be less than or equal to $n_{\mathrm{fwd}}$, which has the value of argument nwl as used in the computation of the wavelet coefficients using nag_mldwt (c09ccc). The data will be reconstructed to level $\left(\mathbf{nwl}-\mathbf{nwlinv}\right)$, where level $0$ is the original input dataset provided to nag_mldwt (c09ccc).

Constraint: $1\le \mathbf{nwlinv}\le n_{\mathrm{fwd}}$, where $n_{\mathrm{fwd}}$ is the value used in a preceding call to nag_mldwt (c09ccc).

2:     lenc – IntegerInput

On entry: the dimension of the array c.

Constraint: $\mathbf{lenc}\ge n_c$, where $n_c$ is the total number of coefficients that correspond to a transform with nwlinv levels and is unchanged from the preceding call to nag_mldwt (c09ccc).

3:     c[lenc] – const doubleInput

On entry: the coefficients of a multi-level wavelet transform of the dataset.

Let $q\left(\mathit{i}\right)$ be the number of coefficients (of each type) at level $\mathit{i}$, for $\mathit{i}=n_{\mathrm{fwd}},n_{\mathrm{fwd}}-1,\dots ,1$. Then, setting $k_1=q\left(n_{\mathrm{fwd}}\right)$ and $k_{\mathit{j}+1}=k_{\mathit{j}}+q\left(n_{\mathrm{fwd}}-\mathit{j}+1\right)$, for $\mathit{j}=1,2,\dots ,n_{\mathrm{fwd}}$, the coefficients are stored in c as follows:

$\mathbf{c}\left[\mathit{i}-1\right]$, for $\mathit{i}=1,2,\dots ,k_1$

Contains the level $n_{\mathrm{fwd}}$ approximation coefficients, $a_{n_{\mathrm{fwd}}}$.

$\mathbf{c}\left[\mathit{i}-1\right]$, for $\mathit{i}=k_1+1,\dots ,k_2$

Contains the level $n_{\mathrm{fwd}}$ detail coefficients $d_{n_{\mathrm{fwd}}}$.

$\mathbf{c}\left[\mathit{i}-1\right]$, for $\mathit{i}=k_j+1,\dots ,k_{j+1}$

Contains the level $n_{\mathrm{fwd}}-\mathit{j}+1$ detail coefficients, for $\mathit{j}=2,3,\dots ,n_{\mathrm{fwd}}$.

The values $q\left(\mathit{i}\right)$, for $\mathit{i}=n_{\mathrm{fwd}},n_{\mathrm{fwd}}-1,\dots ,1$, are contained in dwtlev which is produced as output by a preceding call to nag_mldwt (c09ccc). See nag_mldwt (c09ccc) for details.

4:     n – IntegerInput

On entry: $n$, the length of the data array, $y$, to be reconstructed. For a full reconstruction of nwl levels, where nwl is as supplied to nag_mldwt (c09ccc), this must be the same as argument n used in the call to nag_mldwt (c09ccc). For a partial reconstruction of $\mathbf{nwlinv}<\mathbf{nwl}$, this must be equal to $\mathbf{dwtlev}\left[\mathbf{nwlinv}+1\right]$, as returned from nag_mldwt (c09ccc).

5:     y[n] – doubleOutput

On exit: the dataset reconstructed from the multi-level wavelet transform coefficients and the transformation options supplied to the initialization function nag_wfilt (c09aac).

6:     icomm[$100$] – const IntegerCommunication Array

On entry: contains details of the discrete wavelet transform and the problem dimension for the forward transform previously computed by nag_mldwt (c09ccc).

7:     fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_ARRAY_DIM_LEN

On entry, lenc is set too small: $\mathbf{lenc}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{lenc}\ge ⟨\mathit{\text{value}}⟩$.

NE_BAD_PARAM

On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.

NE_INITIALIZATION

Either the initialization function has not been called first or array icomm has been corrupted.

Either the initialization function was called with $\mathbf{wtrans}=\mathrm{Nag\_SingleLevel}$ or array icomm has been corrupted.

On entry, n is inconsistent with the value passed to the initialization function: $\mathbf{n}=⟨\mathit{\text{value}}⟩$, n should be $⟨\mathit{\text{value}}⟩$.

NE_INT_2

On entry, $\mathbf{nwlinv}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{nwlinv}\ge 1$.

On entry, nwlinv is larger than the number of levels computed by the preceding call to nag_mldwt (c09ccc): $\mathbf{nwlinv}=⟨\mathit{\text{value}}⟩$, expected $=⟨\mathit{\text{value}}⟩$.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example